2 research outputs found
Online codes for analog signals
This paper revisits a classical scenario in communication theory: a waveform
sampled at regular intervals is to be encoded so as to minimize distortion in
its reconstruction, despite noise. This transformation must be online (causal),
to enable real-time signaling; and should use no more power than the original
signal. The noise model we consider is an "atomic norm" convex relaxation of
the standard (discrete alphabet) Hamming-weight-bounded model: namely,
adversarial -bounded. In the "block coding" (noncausal) setting, such
encoding is possible due to the existence of large almost-Euclidean sections in
spaces, a notion first studied in the work of Dvoretzky in 1961. Our
main result is that an analogous result is achievable even causally.
Equivalently, our work may be seen as a "lower triangular" version of
Dvoretzky theorems. In terms of communication, the guarantees are expressed in
terms of certain time-weighted norms: the time-weighted norm imposed
on the decoder forces increasingly accurate reconstruction of the distant past
signal, while the time-weighted norm on the noise ensures vanishing
interference from distant past noise. Encoding is linear (hence easy to
implement in analog hardware). Decoding is performed by an LP analogous to
those used in compressed sensing